Tính : 1 x 1 x 1 x ................ x 1 (có 2017 số 1)
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Xét : 2017.2017 = (x+y+z).(1/x+y + 1/x+z + 1/y+z)
= x/y+z + y/x+z + z/x+y + 1 + 1 + 1
= x/y+z + y/x+z + z/x+y + 3
=> A = x/y+z + y/x+z + z/x+y = 2017^2 - 3 = 4068286
Tk mk nha
Ta có :(x+y+z)(1/x+y + 1/y+z + 1/x+z) =20172
=>x/x+y +y/x+y +z/x+y + x/y+z + y/y+z + z/y+z +x/x+z + y/x+z + z/x+z=20172
=>(x/x+y + y/x+y)+(y/y+z + z/y+z)+(x/x+z + z/x+z)+(x/y+z + y/x+z + z/x+y) =4068289
=>1+1+1+A=4068289
=>A=4068286
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{2017\cdot2019}\)
\(A=\frac{1}{2}\left(\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{2017\cdot2019}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2017}-\frac{1}{2019}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{2019}\right)\)
\(A=\frac{1}{2}\cdot\frac{2014}{10095}\)
\(A=\frac{1007}{10095}\)
\(A=\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{2015\cdot2017}+\frac{1}{2017\cdot2019}\)
\(2A=\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{2015\cdot2017}+\frac{2}{2017\cdot2019}\)
\(2A=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2015}-\frac{1}{2017}+\frac{1}{2017}-\frac{1}{2019}\)
\(2A=\frac{1}{5}-\frac{1}{2019}\)
\(2A=\frac{2014}{100095}\)
\(A=\frac{2014}{10095}:2=\)TỰ TÍNH
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)}{\frac{1}{x+y+x}}=1\Leftrightarrow\left(x+y+z\right)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{x}\right)=1\)
\(\Leftrightarrow\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{x+y+z}\)
\(\Rightarrow\left(\frac{1}{x}+\frac{1}{y}\right)+\left(\frac{1}{z}-\frac{1}{x+y+z}\right)=0\)
\(\Leftrightarrow\frac{x+y}{xy}+\frac{x+y}{z\left(x+y+z\right)}=0\)\(\Leftrightarrow\left(x+y\right)\left[z\left(x+y+z\right)+xy\right]=0\)
\(\Leftrightarrow\left(x+y\right)\left(y+z\right)\left(x+z\right)=0\)
B=\(\left(x+y\right)\left(y+z\right)\left(z+x\right).M=0\)
= 1 nhé
= 1 nhé